Unit 5 Reflection

We started off this unit by learning about work and power. Work = force x distance. Work is measured in units of Joules (Newton meters). An important thing to know about work is that the force and the distance must be parallel, or in the same direction for work to be done. If you lift a box, you are doing work on the box. However, once you have lifted the box up, if you walk with it you are no longer doing work on the box because the force is upward, or vertical, while the direction is horizontal. They are not in the same direction. Therefore, when you are going up a staircase, to find how much work you are doing, you take the force of gravity on you (your weight) and multiply it by the vertical distance of the stairs as you are exerting your force in the upward/vertical direction.

The person going up the stairs has a weight of 600 N, therefore they are exerting 600 N of force when they go up the stairs. The stairs have a vertical distance of 4m. Work = force x distance, so work = 600 N x 4 m = 2400 Joules. This is how much work they are doing to go up the stairs. 

Say you wanted to know how much power they generated walking up the stairs. The equation to use is: power = work / time. The person took 2 seconds to get up the stairs. Power = 2400 J / 2 s = 1200 watts of power. Watts, or J/s, are the units for measuring power. It can also be measured in horsepower which is what we use for the engines of cars, etc. 1 horsepower = 746 watts.

Next we learned about energy, which means "work in" or the ability of an object to do work. Kinetic energy is the energy of movement. You need movement to do work (w = f x d) and KE is measured in Joules. The equation for kinetic energy is: KE = 1/2 m v ^2. The change in KE is equal to work. (∆KE = work). One great application of this information is an alternate way of answering the question why do airbags keep us safe?
When you are in a car crash, you go from moving to not moving regardless of what you hit, therefore the change in kinetic energy is the same regardless of what you hit.
KE = 1/2mv^2
∆KE= KE final - KE initial
∆KE = work
Since the ∆KE is the same and this change is equal to the work done, the work is the same regardless of what you hit. Since work is the same no matter what you hit, the longer of a distance it takes to stop you, the less force is done on you.
work = force x distance
airbag: work = force x distance
dashboard: work = Force x distance
The airbag is soft so it sinks in when you hit it, thus increasing the distance it takes to stop you. Therefore there is a very small force on you, compared to the dashboard which is hard. The less force, the less injury. This is why airbags keep you safe. 
My group did our podcast on the relationship between work and kinetic energy. In addition to explaining the infamous airbag problem, we also talked about the change in kinetic energy. Watch the video below for more!

But the energizer bunny never stops and neither does our physics class- especially not when we're talking about work and energy! We also learned about potential energy. PE = mass x gravity x height. Potential energy is the energy of position; if an object has an height, it has potential energy. If an object is at rest it has potential energy (not kinetic because the velocity of an object at rest is 0 m/s so the KE is zero). As an object falls, its potential energy decreases and its kinetic energy increases. A good way to put this is to say that all the potential energy is transferred into kinetic energy. When the object goes back up to its original height, it gains back all of its potential energy. ∆KE = ∆PE. You cannot gain more energy than the amount that you start with. You can, however, lose some of this energy if the object does not have a 100% efficient energy transfer or if there is friction or air resistance. Lost energy is let off as heat, sound, or light. This is why our car engines hum when we drive around- they are very inefficient.

The ball starts with 20 J of PE and 0 J of KE and falls 10 cm. Because ∆PE=∆KE, due to the conservation of energy, and the ∆PE is 20 J, the ∆KE is from 0J to 20J at the bottom of the ball's path. As the ball falls, it loses PE which turns into KE. When it rises back up the opposite happens. Assuming that the ball has 100% efficiency of energy transfer, the ball will rise up 10 cm to its original height because it must go this high to regain all of its PE. If the ball did not have such an efficient transfer, it would lose height.

The picture above shows how roller coasters have conservation of energy even when they have lots of different sizes of hills. As long as all of the hills are smaller than the first one, the potential and kinetic energies will continue to transfer with an equal amount of energy and the roller coaster will keep rolling. (Note: all of the values were made up for this picture and are not exact).

Finally, we learned about machines. Machines were created and designed to make our lives easier. A common misconception is that machines decrease the amount of work we have to do. This is wrong. Machines make it easier for us to do work by increasing the distance over which we do the work so that we can get the same results by exerting less force.

In the picture below, the inclined slope ( a simple machine) increases the distance of the work 4x. The original vertical height is 1 meter and the distance of the machine is 4 meters. This would allow you to only have to use 1/4 of the force. If you are trying to push a 600 N box up the ramp, the ramp makes it so you don't have to use 600 N of force to do this because you are doing the same amount of work in as work out, similar to the conservation of energy. The distance in is 4m, as compared to the distance out of 1m which is how heigh the box is actually lifted although you accomplish this in 4m slanted. 

The concept of work in = work out is also similar to the conservation of energy because the work out can never be more than the work in but it can be less than the work in depending on how efficient the machine is. The equation to find the efficiency of the work done is: work out / work in x 100. This should give you a percent efficiency.

What I found the most difficult about what we have studied was the conservation of energy. The transfer from potential to kinetic energy was hard for me to grasp; the roller coaster problem was especially difficult to understand.  It confused me how the height increased and decreased again and again but the roller coaster still had the same amount of energy the entire way, even though the amounts of potential and kinetic energy changed depending on its height and position. Drawing the picture in more detail was what helped me finally get it. I am a visual learner through and through. Seeing the different kinetic and potential energies written at the different points of the ride helped me to see that the energies would always add up to the original amount of energy, it was just in different proportions.

At first, it was also hard for me to understand how you could not be doing work on a book that you were carrying if you were moving it forward but now I understand that the force you are doing on the book is vertical because gravity is pulling it down and you are pushing it up (that concept is a bit of a flashback, we learned about action-reaction pairs last semester). You are moving forward so the distance is horizontal and there can be no work because the force and distance are perpendicular and not parallel.

My problem solving skills could have been better in this unit. But I am not too upset that I did not labor over the more difficult problems in this unit. Oftentimes I need a break from a concept before I can understand it. This was definitely true for this unit. When I did not understand the roller coaster problem, I set it aside and came back to it later in more detail and that is when it clicked. However, in the next unit I will spend more time trying to work through the details of harder problems and things that I do not understand. I think this will help me grasp the concepts of the unit in more depth and also allow me to be more engaged in class. I did all of my homework and spent a decent amount of time completing it. I also think I put in a lot of effort to the larger assignments such as blog posts and our podcasts. I got really into finding different ways to present the material- that is why my blog post about machines has two different videos in it. They were both just really cool! And I love Bill Nye, he's great. My confidence in physics faltered a bit this unit, however, as I feel that I did not grasp many of the concepts immediately which is not the case usually. This is another reason why I have a goal of spending more time working through problems in the next unit. I will better understand the material and thus be more confident in my work, which is always a good thing. The airbag problem was one thing that I did not understand at first but through repetition and revisiting it, I finally got it and it helped me with my articulation when writing out and explanation. I have found that using the relevant equations in my explanation really helps me stay on topic and to explain the concept.

This is kind of a stretch, but I connected this unit to every day life because the work that you put into things is the work that you get out, or the results that you see. If i work hard in physics, I will see satisfactory results!

My goals for the next unit are:

1) Bring a positive attitude to class every day.

2) Spend more time on my work (especially hard problems).

3) Study in advance- start reviewing material as soon as we finish one section of the unit. This will be good for the test, the podcast, and our quizzes.

4) Go to conference period to ask Mrs. Lawrence and Mr. Rue for more challenging problems that will help me to further my understanding of the topics and better prepare me for the unit test.

Machines

 

The video above is all about how machines make our lives easier. This is true, not because machines allow us to do less work, but they allow us to do the same amount of work while exerting less force. Work = force x distance. When you increase the distance, as you do with inclined planes and pulleys, you do not need to exert as much force to do the same amount of work. All machines function this way for us. When finding out how much work you are doing on a machine, you must keep in mind that the work in = the work out. Therefore, the force in x the distance in = the force out x the distance out. This is an important equation. I liked the song in the video not only because it is really catchy but also because it provides a lot of real world examples such as a kitchen knife, a wedge, which increases the distance of the force. Although it covers a lot of machines we have not yet studied, it is a good resource.

I also included this Bill Nye the Science Guy video because he talks about simple machines, especially the lever, and shows a lot of cool examples. I also think the explanation and information in this video is a bit easier to follow than the information in the song. Hopefully these two videos combined give you some solid base knowledge of simple machines and how they make your job easier.

Work and Power

Work = force x distance
Work is an important physics concept as it has to do with both the transfer of energy and the use of power which are both things we deal with in everyday life. 
Power = work / time
Power is a word we use all the time to describe electricity and the capabilities of various machines. Power refers to how quickly work is done.

This video describes work and power almost exactly how we learned it in class so I thought it was a helpful recap. It also ties the concepts together well; he presents work and power as being related and things that have to go together instead of two different concepts that happen to have to do with each other.

Unit 4: A Wrap Up

In this unit, I learned about a variety of concepts involving rotation. For starters, we learned about tangential and rotational speed. Tangential velocity is the linear speed of something moving along a circular path. Rotational velocity involves the number of rotations an object makes per minute.

The farther from the center, the more an object’s tangential speed increases. This is because there is more mass farther away from the axis of rotation so the object rotates slower- but this has to do with rotational inertia, which I will explain in a moment.

The difference between rotational and tangential speed is that tangential speed increases the farther away from the center the object is, but rotational speed remains the same no matter where the object is. For example, if one person is close to the inside of a merry-go-round, and their friend is riding a horse along the outside, the friend on the outside will have a faster tangential velocity but they will be moving at the same rotational speed. Additionally, if two objects are the same size, they have the same rotational speed. When two objects are different sizes, it is possible for them to have the same rotational speed but different tangential speeds, like the gears shown below:

Although the picture shows circles, imagine that they are gears that interlock. Because they are connected, a point along the edge of the larger gear will cover the same distance as a point on the edge of the smaller gear in an amount of time, meaning that they have the same tangential velocity. However, the smaller gear will be able to rotate once in a shorter amount of time than the larger gear. In fact, these gears share a 1:3 ratio; meaning that the rotational velocity of the smaller gear is faster than that of the larger gear and the smaller one will rotate completely three times in the time it takes the larger gear to rotate once.

Conversely, objects can also have the same rotational velocity and different tangential velocities. Just like on the merry-go-round, this applies to train wheels. They are tapered so that one side of the wheel is wider than the other and two wheels of this shape are connected. Since the sides are connected, they have the same rotational velocity. The wider part of the wheel has a higher tangential velocity and moves faster because it is farther away from the center than the smaller sides of the wheels. This higher tangential velocity causes the wider part of the wheel to curve inward so that the rails are off-center. When one side of the wheel curves, this causes the other side to curve as well and the wheel self corrects. This is why trains sway on the tracks.

Another related concept is that of rotational inertia. This is the property of an object to resist changes in spin (similar to linear inertia which is the property of an object to resist changes in motion). Rotational inertia depends where the mass is located, or the distribution of mass. As I said before, the farther away the mass is from the axis of rotation, the harder it is for an object to spin- aka, the more rotational inertia it has. If the mass is close to the center/axis of rotation, the object has little rotational inertia. When a runner is trying to go faster, they bend their legs. This brings their leg closer to their hip, which is the axis of rotation. Bringing their leg closer brings the mass closer, so the leg/hip system has less rotational inertia and it is easier to rotate/run. The less rotational inertia and object has, the faster its rotational velocity. This allows the runner to go faster. This concept also applies to ice skaters when they do their big finishes with crazy spins.

When an ice skater has her arms spread out and her legs are wide, her mass is distributed farther from her body (axis of rotation) so she has more rotational inertia and she has a low rotational velocity- she is spinning slowly. Then she brings her arms and legs in to her body, drawing the mass in closer to the axis of rotation and decreasing the rotational inertia, allowing her to spin faster. This brings us to the concept of angular, or rotational, momentum. Angular momentum = rotational inertia x rotational velocity. Just like the conservation of linear momentum, there is conservation of angular momentum. When there is a change in an object’s spin, the momentum is the same before and after. So if the ice skater has a high rotational inertia and a low rotational velocity before, and she has a low rotational inertia after, she must also have a high rotational velocity after to equalize the equation and make the momentum before and after her change in spin the same.

Angular Momentum before = Angular Momentum after

Rotational inertia x rotational velocity = rotational inertia x rotational velocity

So by this point, we know a lot about rotation and how it affects an object’s movement. But what causes rotation?

Torque, ladies and gentlemen, causes rotation. A torque is a force exerted over the distance from the axis of rotation. This distance is called a lever arm.

Torque = Force x Lever Arm

There are three ways to increase torque, and therefore increase the rotation of said object:

11)   Increase the force on the object

22)   Increase the lever arm

33)   Increase both the force and the lever arm

The Forces on both sides of the rod being balanced in the picture above are equal. Their lever arms are also equal. This means that they have equivalent forces on both sides of the rod so it is balanced. If one side had a greater torque than the other, this would cause a rotation and the rod would no longer be balanced. Also, if one side had a greater force than the other side but the other side had an equally greater lever arm, the forces would be equal.

Torque = Torque

Force x lever arm = Force x lever arm

(Just like the conservation of momentum)

As a side note, the force must be perpendicularly applied to the lever arm. Torque is measured in units of Newton meters (Nm).

One thing you will notice in the picture above that I have not yet talked about, is the center of gravity. The center of gravity is essentially the same as an object’s center of mass, which is the average position of all the object’s mass. When gravity acts on this exact point, it becomes the object’s center of gravity. This is actually what keeps us from falling over. As long as our center of gravity is above our base of support, there is no lever arm and without a lever arm, no torque can be generated, meaning there is no rotation and we don’t fall over.

In sports, it is easy to be knocked over. But if you change either your center of gravity or your base of support, it is harder to be knocked over. Bending your knees lowers your center of gravity so it is harder to push it out from above the base of support as has been done to the box in the picture above. If you stand with your feet planted at least shoulder width apart (larger than your natural stance) this widens your base of support, which also makes it harder to displace the center of gravity outside the base of support. These two adjustments make it much harder to knock you over.

Lastly, we learned about centripetal and centrifugal forces. Centripetal force is a center seeking force. It is the force acting on you, pulling you into a curve. When an object moves, its velocity is always straight. Combined with a centripetal force equal to the velocity, the object can follow a curved path. This is why the moon orbits the Earth (the centripetal force being the pull of Earth’s gravity).

Centrifugal force is a “center fleeing force,” but it is a fictitious force. It is only the feeling of your body responding to the centripetal force pulling you inward. For example, when you are riding in a car, you are moving forward. According to Newton’s 1^st Law of Motion, when an object is in motion, it tends to stay in motion unless acted upon by an outside force. (This is where your inertia comes in! Linear, not rotational). When car you are in turns, your body continues to move forward because 1) velocity is always straight and 2) you have inertia, which causes you to resist changes in motion. Only when the car door pushes into you and forces you to turn with it do you turn. This is the centripetal force acting on you. The feeling of your body not wanting to turn is what we refer to as centrifugal force but it is not actually a force. With a group of classmates, I made a podcast that explains even more clearly the concepts of centripetal and centrifugal forces:

The most difficult thing about what we have studied in this unit has been grasping the visualizations of certain concepts. I am primarily a visual learner so this was a little challenging at times. For example, I have seen ice skaters and we watched videos of ice skaters spinning and getting faster, but I do not know what a train wheel actually looks like aside from the strange diagrams and drawings we looked at in class. Sure, I’ve seen a train wheel before, but not from the angle we were considering. This made the concept of train wheels and their tangential velocities hard to understand at first. I overcame this by just accepting what Mrs. Lawrence was teaching me and applying the concepts to the picture I was provided. Eventually the idea cleared up and I grasped the concept. All it really took was for me to open up to a new perspective.

I think my effort towards homework and quizzes improved noticeably this unit. I studied for nearly all of the small quizzes we took and I spent a lot of time writing out my homework and forming really thorough answers which paid off as it aided in my understanding of the lessons. This boosted my confidence in class when we were discussing some harder problems. Also it developed my communication; I feel pretty good about explaining the information in this unit because I spent so much time explaining it to myself and writing out these explanations in a way that I can go back and read in a few months and still get it. I also think that my group for this podcast collaborated more efficiently and easily than my groups in the past. I am really glad that I will be working with the same group for a little while because I think we work well together and I would say this is one of the more articulate podcasts that I have been a part of making.

My goal for the next unit is to spend more time on my podcast and do something a little more unique. I also am going to have a more positive attitude in class!

I liked this unit a lot, even though I did not immediately “get” everything we talked about. I love sports and just about everything in this unit can be applied to my main sports- I run, so now I understand why bending my legs more will help with sprinting. In playing soccer, I will definitely widen my stance and bend my knees more to keep from being knocked down- which seems to happen to me a lot. Also I have been catching even more physics mistakes in song lyrics since this unit. Yay for physics!

Balancing Act

As we are learning about torque and center of gravity, we are also conducting a lab. Our goal is to find the mass of a  meter stick using only the stick itself and a 100 gram lead weight. We are not allowed to use a scale to find the mass of the meter stick. 

Step 1:

When an object is balanced, the torques on either side of its center of gravity are equal. This means that, collectively, the force and lever arm on either side of the center of gravity are the same. However, one side of the stick could have a long lever arm and little force while the other side could have a lot of force with a short lever arm. As long as the counter-clockwise torque on one side equals the clockwise torque on the other side the object will be balanced because neither rotation overpowers the other so the object will not rotate either way.

When the meter stick is placed on a table with some of it hanging off the edge, the center of gravity (for my group's stick) was at the 50.25 centimeter mark on the stick. This is the point that sits on the very edge of the table where part of the stick can hang off without causing any rotation. 
When a mass is placed on the edge of the meter stick, the center of gravity is shifted to the 29.5 centimeter mark. The distance from the stick's actual center of gravity to the edge of the table, where the new center of gravity is, is now its lever arm, instead of being from the center of gravity to the end of that side of the stick. This means the lever arm is much smaller and that the force on the stick is at the end of this lever arm, not at the end of the stick.

Step 2:

We started with what we already knew about torque and balanced objects. When an object is balanced, the torques on either side of its center of gravity are equal. Therefore, it was essential that:

counter clockwise torque = clockwise torque

Since torque = force x lever arm...

force x lever arm = force x lever arm

Not only were these equations going to be important for us to use, so was the equation for weight, since the whole purpose of the lab was to find the mass of the meter stick. It is:

weight = mass x gravity (w=mg)

We kept in mind the units of all the variables we would be working with.

Weight: Newtons (also in kilogram meters per second squared: kg m/s^2)

Mass: grams and kilograms (100 grams equals 0.1 kilogram)

Gravity: 9.8 meters per second squared (m/s^2)

Force: Newtons

Lever Arm: centimeters (but usually we work in meters for lever arm)

Torque: Newton centimeters (N cm; usually it would be Newton meters)

We chose to use our knowledge of torque for this experiment and our calculations because we knew that force and weight are both in Newtons and are equal. So if we could figure out the torque of one side, we would know both the force on that side (because we could just measure the lever arm and find the force through simple math) and the torque of the other side of the center of gravity because the two torques would be equal). Using this knowledge, we could find the mass through the equation for weight. In order to complete these processes, we took measurements. We found the length of all the lever arms and the point where the center of gravity was. We also found the mass of the weight placed on the meter stick, both in grams and kilograms.

Measurements:

Center of gravity = 50.25 cm mark

Center of gravity with the weight o the meter stick = 29.5 cm mark

Mass of weight = 100 grams (0.1 kilograms)

Lever arm to the left of new center of gravity = 29.5 cm (as shown in picture above)

Lever arm to the right of new center of gravity = 20.75 cm (as shown in picture above)

Step 3:

After we had all of our preliminary measurements taken and our plan of action was established, we began calculating. First, we found the force on the left side of the center of gravity with the weight. Here are our calculations:

w=mg

  = 0.1kg (9.8 m/s^2)

  =0.98 N = Force

Then we found the torque on this portion of the ruler...

torque = force x lever arm

            = (0.98 N)(29.5 cm)

            = 28.91 N cm

Now it was time to find the torque of the other side of the center of gravity...

counter-clockwise torque = clockwise torque

                      [ 28.91 N cm = 28.91 N cm]

               force x lever arm = force x lever arm

              (0.98 N)(29.5 cm) = F (20.75 cm)

                        28.91 N cm = F (20.75 cm)

                                1.39 N = F

Since Force = weight...

1.39 N = weight

weight = mass x gravity

1.39 N = mass (9.8 m/s^2)

0.1418 kg = mass (b/c N also equal kg m/s^2 so when divided, the units cancelled out to kg)
141.8 g = mass
This was our calculated mass (141.8 grams) which we checked on the scale after the experiment concluded. The actual mass of the meter stick was 142.9 grams, so we were very close (only 1.1 grams off).

Torque and Center of Mass

A torque causes rotation. Torque = force x lever arm (the distance of the force from the axis of rotation). The example shown in the video demonstrates torque well as it shows the two sides of the ruler have the same lever arm and their torques are equal so the ruler is balanced on his finger. When I say the torques are "equal," I mean that the counter-clockwise torque on the left side of the ruler and the clockwise torque on the right side of the ruler are equal to each other so they balance each other out. This video, although it does not go into detail, also shows the center of mass. The center of mass is the average position of all the mass of an object. When gravity acts on this point, it is the object's center of gravity. The object's center of gravity is right where the man is supporting the ruler with his finger, which is another reason why it is balanced. 
I think this video is a good resource because it explains torque very clearly and in a lot of detail. The end of the video is actually more advanced than the material we covered in class; we did not learn about the equations he uses. But despite this, I think the rest of the video is clear and helpful. The demonstration shows torque really well, as well as center of gravity even though it does not explicitly go into detail about center of gravity.

Rotational/Angular Momentum

Having already learned about momentum and the conservation of momentum, my class recently learned about angular, or rotational, momentum. To understand rotational momentum, you must first know about rotational inertia. Rotational inertia is the property of an object to resist changes in spin (rotation). The more mass an object has, the greater its rotational inertia is. This also involves the distribution of the mass. When the mass of an object is far away from the axis of rotation, the rotational inertia is greater. When the girl in the video is starting to spin, she keeps her arms extended. This causes her mass to be spread out from her body, where her axis of rotation is, so she spins slowly at first. When she pulls her arms and legs into her body, this changes the distribution of mass so that it is closer to the axis of rotation. She then has a smaller rotational inertia and spins very quickly.

But wait, there's more...

Just as linear momentum is conserved, there is conservation of rotational momentum as well. The total rotational momentum of an object before the change in spin must be equal to the total rotational momentum of the object after the change in spin. Rotational momentum is equal to rotational inertia  x rotational velocity. In the video, we could see how the girl's rotational inertia changed (which I explained) and how it directly affected her velocity. Before the change in her spin, she had a large amount of rotational inertia and a subsequently small rotational velocity. After the change in spin, her rotational inertia was much smaller, and in accordance with conservation of rotational momentum, her rotational velocity increased so that the total momentum was the same before and after the change in spin.

I think this video clearly shows the change. The demonstration would be perfect if there were arrows showing her inertia and such, but I think this is a great rotational momentum resource when coupled with an explanation.